Edgeworth expansions for centered random walks on covering graphs of polynomial volume growth
Probability
2023-06-05 v2
Abstract
Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the underlying graphs but also the modified harmonic embedding of the graph into a certain nilpotent Lie group. Moreover, we apply the rate of convergence in Trotter's approximation theorem to establish the Berry-Esseen type bound for the random walks.
Keywords
Cite
@article{arxiv.2011.13783,
title = {Edgeworth expansions for centered random walks on covering graphs of polynomial volume growth},
author = {Ryuya Namba},
journal= {arXiv preprint arXiv:2011.13783},
year = {2023}
}
Comments
37 pages